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On norms, spread, characteristic polynomial and determinant of Hankel and Toeplitz matrices with Mersenne sequence | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 08 دی 1403 اصل مقاله (416.28 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.30037.2287 | ||
| نویسندگان | ||
| Kalika Prasad1؛ Munesh Kumari* 1؛ Jagmohan Tanti2 | ||
| 1Department of Applied Science and Humanities (Mathematics), Government Engineering College Bhojpur, Bihar, India, 802301 | ||
| 2Department of Mathematics, Babasaheb Bhimrao Ambedkar University, Lucknow, India, 226025 | ||
| چکیده | ||
| In this work, some new properties of the Hankel and Toeplitz matrices are obtained by considering the Mersenne numbers as entries. We developed efficient formulas to compute matrix norms like $\|.\|_1$, $\|.\|_\infty$, Euclidean norm, spread, and the lower and upper bound for the spectral norm of these matrices. Also, the study shows that these matrices are non-singular for $n=2$ and singular for $n\geq 3$. Furthermore, we presented rank, eigenvalues, principal minors, and the characteristic polynomial of them explicitly. | ||
| کلیدواژه‌ها | ||
| Mersenne and Fermat numbers؛ Recursive matrices؛ matrix norms and spread؛ rank؛ characteristic polynomial | ||
| مراجع | ||
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